ON THE GENERAL CIRCULATION OF THE ATMOSPHERE. 181 
times. This happens in consequence of the acceleration of the rotat- 
ing mass while approaching the center of attraction of the fixed mass, 
and the corresponding retardation which it experiences in departing 
from it. The greater velocity derived from the acceleration results in 
the description of a greater are in a unit of time, and leads therefore 
to the laws of areas. Now, according to Ferrel, a mass of air rotating 
with the earth’s surface in any latitude, when displaced northward or 
southward, can not, as IL understand it, continue its course with its 
absolute velocity unchanged, as would be the case in the conservation 
of its vis viva, but its moment of rotation must remain constant, which 
corresponds to an important change of velocity. In order that the 
moment of rotation shall remain constant—which will be the case if 
the linear velocity of the rotating body changes in such a way that 
equal surfaces are described by it in equal times—there must be ex- 
pended a considerable amount of energy in order to effect the change 
of velocity of the inert mass. But the force that could do this work 
is quite lacking. If we shorten the radius of rotation of a rotating 
solid mass, then the force which causes the shortening must overcome 
the centrifugal force. The sum of the products of all the centrifugal 
forces overcome by the paths traversed gives the work performed in 
accelerating the rotating mass, and this is sufficient to maintain the 
law of surfaces; that is, here the moment of rotation is constant. But 
in the motion of the air upon the earth’s surface, no analogous relations 
subsist. In a tangential displacement on the earth’s surface, no change 
ot gravity takes place and no acceleration of the displaced mass by 
gravity. Itis just as difficult to-understand by what means a pres- 
sure upon them of neighboring air layers should arise for displacing, 
which would be able to do the enormous work of acceleration that the 
conservation of the moment of rotation requires! 
A displacement of the whole air mass of a rotating ring in a north 
or south direction is not practicable, since the volume of such a ring of 
given thickness changes with the cosine of the latitude. Thus in a 
poleward displacement, a corresponding part of the mass of the ring 
must remain behind—relatively, must return to the equator. But also 
for the portion of the ring of air actually displaced toward the pole, no 
physical reason can be found why the conservation of its moment of 
rotation must be assumed. On the contrary, this assumption would 
lead to the greatest contradictions and discontinuities; for, in the 
assumed original condition in which no meridional currents yet existed, 
from which Ferrel as well as | have proceeded, the air rotated at each 
latitude with the velocity of the ground upon which it was at rest. 
The velocity of the masses of air therefore decreased with the cosine of 
the latitude Now, with the appearance of a meridional current, this 
relation, acconding to Ferrel, would not only have to be inverted, but 
instead of a decrease, an increase in the velocity of the air must take 
place at a still higher rate, if the moment of rotation of the air is to 
